Let $G=S_3$. It has 3 irreducible representations: $1, sgn$ and $V$; the trivial rep, sign rep and rep $V$ where $dimV=2$
Consider the subgroup $H=S_2$ with irreps $1_H$ and $sgn_H$
What is the dimension of $Ind_H^G(sgn_H)$?
I know that $|S_3|=6$, $|S_2|=2$ and $|S_3 / S_2|=3$
The induced representation passes from $G$ and $H$ so I suppose dim $\in \{2, 3, 4, 5, 6\}$ but I am unsure